A Galerkin-homotopy method for the distributed parameter estimation problem

A Galerkin-homotopy method is proposed for the distributed parameter estimation problems of partial differential equations. Based on the Galerkin principle, the problem of inverting the parameter is transformed into the problem of estimating a finite dimensional vector formed by the coefficients of the expansion of the parameter on an orthogonal basis. To overcome the local convergence of traditional iterative methods, the homotopy method is introduced and combined with Tikhonov regularization to form a new and widely convergent method. As a practical application, the distributed parameter estimation problem of an elliptical equation is solved. Numerical results show the method's effectiveness.